the purpose of physics, is to predict we still can't predict ther degree's of freedom. so you cannot technically say it is solved. yea sure it is not analytical, But isn't that what we want?
I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature...